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Geomentry-Fundamental concepts-Angles

Posted on 2016-10-10
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Last Modified: 2016-10-21
Dear experts,

I have attached two pic of plane geometry. I am unable to calculate the angles. Can someone please guide me with the calculations.

Thank you
Ex-26A1.JPG
Ex-26A2.JPG
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Question by:Excellearner
3 Comments
 
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by:Dr. Klahn
Dr. Klahn earned 250 total points
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a:  The angles sum to form a line.  Therefore x + y + z = 180 degrees.  x = 3y and 3z = 5x.  Substitute for x into z.  3z = 15y.  Then go back to x + y + z = 180, substitute in the values for x (3y), y and z (5y), and solve.  The equation can be solved in any of the variables, y is just convenient.  Then go back to the definitions and calculate x and z from y.

b:  Solve similarly to a, but in this case the angles sum to a circle, so a + b + c + d + e = 360 degrees.  The remainder of the solution is as above.
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Herman D'Hondt earned 250 total points
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Can I assume these are homework questions? I'll give you a clue that may help you solve the problems.

The reason why you can't solve the equations is that you have more variables than equations, so you need an additional equation. In the first picture you are given 2 equations with 3 variables. To solve it, you need 3 equations. Looking at the picture, there is an obvious 3rd equation that you can write down, something you already know about the 3 variables.

Here are the 3 equations:
x = 3y

3z = 5x
nx+my+pz=a
The values of n, m, p and a are obvious from the drawing. See if you can find them. Once you have them you can go ahead and solve the equations.

The same is true about your 2nd picture: you have 5 variables and 4 equations. You know something else about the 5 variables, which will give you your 5th equation.
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